Problem painting through model in overlapping uv area
Moving the uv's to an unused space will work.

From the blender manual for v2.79 overlapping uv's are not supported:

"Known Limitations

UV Overlap

In general overlapping UVs are not supported (as with texture baking).

However, this is only a problem when a single brush stroke paints onto multiple faces that share a texture."

So the only solution really is to delete the part or move the problem uv's to an area that is not used. The original uv's are set by someone else but since the part is not seen it doesn't matter.